Question 213153
The problem gives you:
s=-16t^6+69t
.
Where s = feet above ground
.
Now, they would like to know at what time (t) is it when it is 54 feet above the ground.  Simply substitute s for 54 and solve for t:
s=-16t^6+69t
54=-16t^6+69t
0=-16t^6+69t-54
0=16t^6-69t+54
Solve by using the quadratic formula.  Doing so yields:
t = {3.285, 1.027} (in seconds)
The reason for two answers -- once going up and another time coming down.
.
Details of quadratic below:
*[invoke quadratic "t", 16, -69, 54 ]